Does a personal bias discredit someone's opinion or scientific work? Maybe not. Not if good scientific methods are used, at least. I don't think that someone's bias is necessarily a problem.
First off, what is a bias? Ultimately it is an inclination to choose one side over an other. So, lets say someone tells me that they own a unicorn. Well, my bias is to not accept that statement as true. My bias is that unicorns are fictitious creatures. For me to change my bias, I'd have to see proof of this creature. So, in this example, my bias causes my to require proof. I'd say that's a good thing.
What if I'm a chemist that is working on a new drug to cure some disease I would have personal interest in the outcomes of the trials, right? If my new drug cures a disease, I could make a lot of money, and I might have an interest in ignoring any negative side effects. In this respect a personal bias could be a bad thing.
It's not that we don't have bias, it's that the methods that we use to acquire knowledge should suppress if not eliminate our own bias. This is what separates good data from bad data. How much has our own bias influenced the data. In terms of scientific studies, this is why we do double blind studies (neither the researcher nor the patient is aware of who is given a placebo and who is given the real medicine until after the study). This is also the purpose of peer review, or other researchers repeating the study to confirm effectiveness.
We are humans, not robots. We can never really get rid of our own bias. But, it could also be our motivating reason why we pursue a scientific investigation in the first place. We might just want to determine whether or not our bias is well grounded. If controls are used correctly then our own bias shouldn't effect any data we collect. So, is bias truly a problem in the realm of science. Absolutely not. Not if the data is able to be isolated from this bias.